$A$ train is moving along the tracks at a constant speed $u$. $A$ girl on the train throws a ball of mass $m$ straight ahead along the direction of motion of the train with speed $v$ with respect to herself. Then

To simulate car accidents,auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \; kg$ moving with a speed $18.0 \; km/h$ on a rough road having $\mu = 0.5$ and colliding with a horizontally mounted spring of spring constant $6.25 \times 10^{3} \; N m^{-1}$. What is the maximum compression of the spring in $m$?

$A$ $2 \ kg$ block slides on a horizontal floor with a speed of $4 \ m/s$. It strikes an uncompressed spring and compresses it until the block is motionless. The kinetic friction force is $15 \ N$ and the spring constant is $10,000 \ N/m$. The spring compresses by ............. $cm$.

$A$ spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \ N \ m^{-1}$ and the mass of the block is $2.0 \ kg$. Ignore the mass of the spring. Initially,the spring is in an unstretched condition. Another block of mass $1.0 \ kg$ moving with a speed of $2.0 \ m \ s^{-1}$ collides elastically with the first block. The collision is such that the $2.0 \ kg$ block does not hit the wall. The distance,in metres,between the two blocks when the spring returns to its unstretched position for the first time after the collision is . . . . .

$A$ force exerts an impulse $I$ on a particle changing its speed from $u$ to $2u$. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is

$A$ pendulum of length $1 \,m$ and having a bob of mass $1 \,g$ is pulled aside through an angle $60^{\circ}$ with the vertical and then released. The power delivered by all the forces acting on the bob when the pendulum makes $30^{\circ}$ with the vertical is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,mW$)